I'm trying to remember in the flashbacks, does Angelus call Spike Spike or William?  I know he calls him William in the mine shaft, and Spike tells him it's Spike now.  But after that?  And are 'Willie' and 'boy' a fanon thing?

in "Destiny" he calls him William but only in a smug and derogotory manner - Drusilla and Angelus keep calling him Willie or Willy (not sure how they spell) but a fun connection to this use of name is with the romantic ballet Sylphide, where the ghosts of  abandoned lovers and women who suffered from unrequited love - they are called "Willis" - not sure if this is the correct spelling, but the tern is right.  In the UK "willy" is an offensive term  for a penis.

Watched Destiny this morning.  Angel(us) does call him Willy, usually when he's being condescending or trying to rile him up.  Angel calls Spike "William" in another episode of AtS Season 5, but I can't remember which one right now.  It's when they're sitting on the couch, and Angel tells Spike that he always liked Spike's poems.  Spike points out that Angel likes Barry Manilow (i.e., Angel has no taste anyway).  Spike also calls Angel Liam in that same scene.  I'm pretty sure this is the only time a character calls Angel by his human name on screen.

i'm pretty sure angel always tryed to call him william
No, Angel called him Spike most of the time... Angelus usually called him William (or Willy to be mean) in the flashbacks, but he called him Spike in season 2.

spike always let buffy call him william

Buffy calls Spike William exactly twice:
1. No Place Like Home: No one has time for this, William.
2. As You Were: I'm sorry, William.

I just looked at another thread where some Guest apparently took a quiz that said Buffy called Spike William three times, not twice, and was asking for the third time. The two above are the only times I remember Buffy calling him William, so I think they should talk to the author of the quiz to find out the third time.

Angelus in Season Two called Spike a lot of nicknames about the wheelchair and Spikey but I don't think he called him Willy. When Angel was pretending to be the old Angelus in "School Hard" he says, "Spike, my boy!"
I think how Angelus spoke to Spike in the early days and after having the soul were different, so he probably called him different things depending on the year.

Maybe the third time she called him William was actually "William the Bloody"? That was in Something Blue: "Now, do you want to be William the Bloody or just Spike? 'Cause either way, it's gonna look majorly weird."

Also, Faith-in-Buffy's-body called him William the Bloody in Who Are You?: "William the Bloody with a chip in his head. I kinda love this town."

Angelus has called him "William" many a time in non derogatory ways, as "The Girl In Question" suggests...

(cut to 1894; Angelus and William the Bloody are in their underwear, hanging from chains in the ceiling)

ANGELUS: (waking up) Oh, William.
(he struggles to swing himself into William)
ANGELUS: Agh! Unh!
WILLIAM: Ow! Bloody hell.
ANGELUS: (struggling against his restraints) Agh! Unh!
WILLIAM: That right bastard.
ANGELUS: The Immortal thinks he can do this to us?
WILLIAM: He doesn't know who he's dealing with.
ANGELUS: Well, he's about to find out. Aagh!
WILLIAM: He's gonna curse the day he ever crossed purpose with Angelus.
ANGELUS: And William the Bloody.
WILLIAM: We'll see just how immortal he is when we're done with him.
ANGELUS: We'll carve him up like a Sunday roast and make him watch as we feast on his steaming flesh.
(they both struggle to get free of their shackles, but make no headway)
ANGELUS: How you doin'?
WILLIAM: Bugger.